Method for determining angular velocity

ABSTRACT

The application relates to a method for measuring the angular velocities about at least two mutually perpendicular axes. 
     For this purpose, a laser gyro, for example, is rotated about an auxiliary axis of rotation at the angular velocity ω o  and the output value of the gyro signal is determined when the gyro is in the rotary position ω o  t, at which one of the components of the output signal of the gyro becomes O. The components of the desired rotation can then be calculated from the resulting system of equations.

The invention relates to a method for determining the angular velocitiesΩ_(I), Ω_(II) and/or Ω_(III) about at least two axes I, II and/or III ofa preferably rectangular coordinate system. These axes may be, forexample, the axles of a vehicle.

It is known to measure the angular velocities about two or even threeaxes that are perpendicular to one another by utilizing correspondinglyplaced gyros. Such a measuring arrangement is expensive.

It is the object of the invention to reduce the expenditures formeasuring at least two angular velocities about mutually perpendicularaxes.

This is accomplished in that a gyro (e.g. a laser gyro) which does notoffer any resistance to rotation about any desired axis is rotated at aknown angular velocity ω_(o) having the known components ω_(oI), ω_(oII)and ω_(oIII) about an auxiliary axis whose orientation in the coordinatesystem is defined by the angles φ and θ, with φ being the angle betweenthe first axis and the projection of this auxiliary axis of rotation inthe plane defined by the first and second axis and θ is the anglebetween the auxiliary axis of rotation and this projection. The inputaxis of the gyro is inclined toward the auxiliary axis by an angle of90[°]-δ and the value for Ω is measured at angular values α=ω_(o) t, atwhich components of the term

Ω=f.sub.[(Ω_(n) +ω_(on), for n=I through III), (φ), (θ), (δ), (sin ω_(o)t) and (cos ω_(o) t)]

representing the output signal Ω of the gyro become zero, with thevalues for Ω_(I), Ω_(II) and/or Ω_(III) being calculated from theresulting equations.

The following term results for the output signal Ω of the gyro: ##EQU1##

Pursuant to the first feature of the solution according to theinvention, a gyro is employed which does not offer any resistance to therequired rotation; a mechanical gyro cannot be used here. The abovestated teaching permits the determination of only two or also threeangular velocities Ω_(I), Ω_(II) and/or Ω_(III). To simplify thecalculation, the auxiliary axis of rotation is placed advantageouslyinto one axis, e.g. into the third axis; then there will be nocomponents of ω_(o) about the other axes. Since φ and θ are zero,Equation (1) above is simplified to:

    Ω=Ω.sub.I cos δ cos ω.sub.o t+Ω.sub.II cos δ sin ω.sub.o t+(Ω.sub.III +ω.sub.oIII) sin δ(2)

It can be seen that with this arrangement it is possible to determineall three components Ω_(I) to Ω_(III) by measuring Ω at cos ω_(o) t₁ =0and sin ω_(o) t₂ =0 and a third value of ω_(t) (ω_(o) t₃), at which thesine or cosine of ωt₃ becomes 0. δ is constant. If δ is made to equalzero, the last term can be omitted and ω_(I) and ω_(II) can bedetermined by measuring Ω at two angles α which differ by 90° (or an oddmultiple thereof).

Preferably, the angular velocity ω_(o) is selected at such magnitudethat it is greater than the greatest possible angular velocities to bedetermined. Only then is it assured that the Ω values determinedsuccessively at various angles of α or possibly δ originate from thesame angular velocity.

Thus, ω_(o) will be selected depending on the case at hand. For use onships, there will occur practically no angular velocities Ω greater thana few radians/sec. In this case, a value of, e.g., 10 revolutions persecond is sufficient for ω_(o). For use in land vehicles, a greaterω_(o) will have to be selected, e.g. 30 to 100 revolutions per second.

Although it is actually sufficient to swing the gyro back and forth overonly a sufficient angular range at ω_(o), continuous rotation willgenerally be preferred. If ω_(o) is constant over the entire range ofrotation, the components resulting therefrom can also be calculated andare constant. If necessary, ω_(o) must also be measured by measuring thetime required for one revolution. If ω_(o) is not constant within theindividual revolution, the curve of ω_(o) during the revolution must bedetermined, e.g. by measuring the times at which a plurality of anglemarkers are reached (e.g. every 30°) and the actual values for thecomponents of ω_(o) must be determined from the resulting curve at thecorresponding angles α_(n) and possibly δ_(n).

In a modification of the invention it is proposed to arrange theauxiliary axis of rotation in space in such a manner that it forms thesame angles with respect to the x, y and z coordinates of the coordinatesystem.

If these angles are each 54.73°, the auxiliary axis of rotation becomesthe axis of rotation or the center axis, respectively, of a cone whosegeneratrix is identical at three points with the coordinate axes.

In a preferred modification of the invention it is proposed to orientthe input axis of the gyro parallel with the generatrix of the cone. Inthis case, the angular velocity about one of the coordinate axes can bemeasured directly if there is a momentary coincidence of the input axiswith that coordinate axis.

One embodiment of the invention will be explained with the aid of thedrawing.

It is shown in:

FIG. 1, an embodiment in which the gyro is rotated about the z axis atω_(o) ;

FIG. 2, the curve of Ω resulting therefrom;

FIG. 3, a block circuit diagram for determining the components of Ω;

FIG. 4, an embodiment in which the gyro rotates on a cone generatrixwhich is tangent on the x, y, [and] z coordinates.

In FIG. 1, a laser gyro is placed in the zero point of an x, y, zcoordinate system. This gyro has an input axis 1 whose momentaryposition is given by the angles α=ω_(o) t between the x axis andprojection 2 of axis 1 on the x-y plane and the angle δ betweenprojection 2 and axis 1. The gyro is rotated about the z axis at aconstant and known angular velocity ω_(o). Thus, axis 1 describes a conegeneratrix about the z axis. A random angular velocity which is to bedetermined with respect to its components Ω_(x), Ω_(y) and Ω_(z) aboutany desired axis 3 is superposed on the rotation about the z axis atω_(o).

Under these conditions, the above stated equation (2) applies. Plottedover the angle α=ω_(o) t which changes due to the rotation about the zaxis, the output signal Ω of the gyro will have the curve shown in FIG.2, i.e. it oscillates about the value (Ω_(z) +ω_(o)) sin δ which resultsfrom the last term of (2) and is dependent on Ω_(z), but constant overα. By determining the values Ω₁ at α₁ =0°, Ω₂ at α₂ =90°, and Ω₃ at α₃=180°, the following equation system results: ##EQU2## The solution ofthese equations provides the unknown values Ω_(x), Ω_(y) and Ω_(z) asfollows: ##EQU3##

In FIG. 3, the gyro is marked 10, a sensor which monitors the rotationof gyro 10 and puts out a trigger signal at α₁, α₂ and α₃ is marked 11,a gate is marked 12 and a computer is marked 13. As soon as the anglevalues α₁ to α₃ are reached, sensor 11 sends trigger signals to gate 12so that the output signals Ω₁, Ω₂ and Ω₃ present at the gyro at thistime reach computer 13 which solves Equation (4) under consideration ofthe constants ω_(o) and δ.

If δ=0, the following equations result from (3):

Ω_(x) =Ω₁ at α=0° and

Ω_(y) =Ω₂ at α=90°.

Thus, in this case, Ω_(x) and Ω_(y) are two components which aredetermined particularly easily.

With the use of a laser gyro, the method according to the invention hasthe particular advantage that an output signal Ω of the gyro appears(e.g. ω_(oIII) sin θ (in case 2)) before a measurable rotation havingcomponents Ω_(I), Ω_(II) and/or Ω_(III) is present. This phenomenonresults in a displacement of the 0 point of the laser gyro: thisphenomenon thus brings about the "side effect" of lock-in suppression,i.e. the avoidance of the inability of the gyro to measure at low ratesof rotation. In this case, δ must be selected in such a manner that witha given ω_(o) the zero point will be displaced sufficiently far into onebranch of the operating characteristic of the gyro.

If δ is permitted to become=90°, a laser gyro results which measuresonly rotation about one axis but likewise exhibits lock-in suppression(e.g. Ω=Ω_(III) +Ω_(oIII) for (2)). This is also a realization which issignificant for the invention and which can be used if individual gyrosare employed.

FIG. 4 shows a laser gyro 1 and its input axis 2. This laser gyro isrotated at a constant speed ω_(o) about axis of rotation 3. Input axis 2is inclined by an angle β=54.73° with respect to the axis of rotation.This value results from the equation

    cos.sup.2 β.sub.1 +cos.sup.2 β.sub.2 +cos.sup.2 β.sub.3 =1

where β₁ =β₂ =β₃. Thus axis 2 describes a cone generatrix and, in threepositions shifted by 120° with respect to one another, lies parallel tothe reactangularly abutting coordinates x, y and z of any desiredcoordinate system. Preferably, this coordinate system is identical withthe coordinate system in which the vector of an angular velocity is tobe determined. This eliminates coordinate transformation and the angularvelocity component Ω of the vector on axes x, y and z, can be determineddirectly by measuring the angular velocities Ω_(I), II, III about inputaxis 2 of the gyro in three positions identical with coordinates x, yand z, according to the equation:

    Ω.sub.x =Ω.sub.I +ω.sub.o cos β

    Ω.sub.y =Ω.sub.II +Ω.sub.o cos β

    Ω.sub.z =Ω.sub.III +ω.sub.o cos β

in which the component of rotation ω_(o) about axis 3 is considered.

When employing a laser gyro, the method according to the invention hasthe particular advantage that an output signal of the gyro appearsbefore a measurable rotation having the components Ω_(I), Ω_(II) and/orΩ_(III) is present. This phenomenon results in a shift of the zero pointof the laser gyro, thus it brings about the "side effect" of lock-insuppression, i.e. avoidance of the inability of the gyro to measure atlow rates of rotation. In this case, ω_(o) must be selected in such amanner that the zero point will be displaced sufficiently far into onebranch of the operating characteristic of the gyro.

I claim:
 1. Method for determining the angular velocities Ω_(I), Ω_(II)and/or Ω_(III) about at least two axes I, II and/or III of a preferablyrectangular coordinate system, characterized in that a gyro which doesnot resist rotation about any desired axis (e.g. a laser gyro) having aknown angular velocity ω_(o) with the known components ω_(oI), ω_(oII)and ω_(oIII) is rotated about an auxiliary axis of rotation whoseorientation in the coordinate system is defined by the angles φ and θ,where φ is the angle between the first axis and the projection of saidauxiliary axis of rotation in the plane defined by the first and thesecond axis and θ is the angle between the auxiliary axis of rotationand this projection, with the input axis of the gyro being inclined withrespect to the auxiliary axis of rotation by an angle of 90-δ; that thevalue for Ω is measured at angle values α=ω_(o) t, at which componentsof the termΩ=f.sub.[(Ω_(n) +ω_(on), for n=I through III), (φ), (θ), (δ),(sin ωt) and (cos ωt)]representing the output signal Ω of the gyrobecome zero and the values for Ω_(I), Ω_(II) and/or Ω_(III) arecalculated from the resulting equations.
 2. Method according to claim 1,characterized in that the auxiliary axis of rotation is placed into oneof the axes I, II or III.
 3. Method according to claim 1, characterizedin that the auxiliary axis of rotation is placed into axis III. 4.Method according to claim 3, characterized in that the angle δ isselected to be zero.
 5. Method according to claim 1 characterized inthat the angular velocity ω_(o) is greater than the highest occurringangular velocity Ω.
 6. Method according to claim 1, characterized inthat the angular velocity ω_(o) is kept constant.
 7. Method according toclaim 1, characterized in that the respective angular velocity ismeasured.
 8. Method according to claim 7, characterized in that thecurve of the angular velocity is determined over the range of the angleof rotation and is utilized for the exact determination of ω_(o) at theangles α_(n), at which Ω_(n) is determined.
 9. Method according to claim1, characterized in that the auxiliary axis of rotation is oriented insuch a manner that the angles β₁, β₂ and β₃ formed between the auxiliaryaxis of rotation and the coordinate axis of the coordinate system areidentical in size.
 10. Method according to claim 9, characterized inthat the angles β₁₋₃ =54.73° and the input axis of the gyro is likewiseinclined by 54.73° with respect to the auxiliary axis of rotation, sothat, if the gyro rotates about the auxiliary axis of rotation, theinput axis lies parallel to the coordinate axes x, y and z in threemomentary positions.
 11. Method according to claim 10, characterized inthat the output signal Ω of the gyro in the three positions I, II, IIIis formed according to the equations

    Ω.sub.I =Ω.sub.x +ω.sub.o cos β.sub.1

    Ω.sub.II =Ω.sub.y +ω.sub.o cos β.sub.2

    Ω.sub.III =Ω.sub.z +ω.sub.o cos β.sub.3

where the angular velocities about axes x, y and z are marked Ω_(x), y,z.
 12. Method according to claim 1, characterized in that only a singlegyro is rotated about the auxiliary axis and the values for Ω_(I),Ω_(II) and/or Ω_(III) are calculated on the basis of the output signal Ωproduced by the single gyro.